• Journal for History of Mathematics
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• v.21 no.2
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• pp.1-18
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• 2008

As a sequel to the previous paper Gou Gu Shu in the 18th century Chosun, we study the development of Chosun mathematics by investigating that of Gou Gu Shu in the 19th century. We investigate Gou Gu Shu obtained by Hong Gil Ju, Nam Byung Gil, Lee Sang Hyuk and Cho Hee Soon among others and find some characters of the 19th century Gou Gu Shu in Chosun.

• Journal for History of Mathematics
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• v.21 no.4
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• pp.1-10
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• 2008

In this paper, we investigate the part dealing with algebra in Hong Gil Ju's GiHaSinSul to analyze his algebraic structure. The book consists of three parts. In the first part SangChuEokSan, he just renames Die jie hu zheng(疊借互徵) in Shu li jing yun to SangChuEokSan and adds a few examples. In the second part GaeBangMongGu, he obtains the following identities: $$n^2=n(n-1)+n=2S_{n-1}^1+S_n^0;\;n^3=n(n-1)(n+1)+n=6S_{n-1}^2+S_n^0$$; $$n^4=(n-1)n^2(n+1)+n(n-1)+n=12T_{n-1}^2+2S_{n-1}^1+S_n^0$$; $$n^5=2\sum_{k=1}^{n-1}5S_k^1(1+S_k^1)+S_n^0$$ where $S_n^0=n,\;S_n^{m+1}={\sum}_{k=1}^nS_k^m,\;T_n^1={\sum}_{k=1}^nk^2,\;and\;T_n^2={\sum}_{k=1}^nT_k^1$, and then applies these identities to find the nth roots $(2{\leq}n{\leq}5)$. Finally in JabSwoeSuCho, he introduces the quotient ring Z/(9) of the ring Z of integers to solve a system of congruence equations and also establishes a geometric procedure to obtain golden sections from a given one.

• (The)Study of the Eastern Classic
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• no.32
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• pp.159-187
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• 2008

This article aims to investigate the change of theories of reading and its historical meaning in the later Joseon period. Three scholar who left major theories of reading are mainly analyzed for the sake of it. Park, Se-chae(1631-1695) was a Neo-Confucianist who had the theory of reading named Dokseo-Gungliron(讀書窮理論). It was totally based on the scheme of Neo-Confucianist instruction and concentrated on mastering the moral principles with relishing the sentences of the Confucian Canons. Jeong, Yak-yong(1762-1836) was a Practical learning scholar and then criticized the moral-centric theory of reading of Neo-Confucianism. He valued much of the Confucian Canons but also focused on erudite reading so as to enlarge practical knowledge. Hong, Gil-ju(1786-1841) was a stylist and presented a severe criticism against Neo-Confucianist theory of reading as much. He thought that what we could realize with reading are the principles of the individual, not of the whole. The change of theories of reading in the later Joseon period as above reveals us the fact that the intellectual history of that period was in the process of dynamical change.